In the case of the temperature measurement, that can be a surface or else internal (volume) temperature measurement. One well known example is the measurement of temperature using passive surface wave piezoelectric sensors, commonly called SAW (Surface Acoustic Wave) sensor. FIG. 1 illustrates the surface of a solid in the presence of a conventional surface acoustic wave: Rayleigh wave.
These sensors are for example composed of resonators operating in frequency bands ranging from 430 to 450 MHz and generally using a quartz substrate making it possible to achieve high quality factors (product Q*f of the order of 6*1012).
A surface wave resonator is composed of metal electrodes, deposited by standard photolithography methods in microelectronics, on the surface of a piezoelectric substrate. FIG. 2 illustrates the electrodes of an SAW resonator seen in cross section in the sagittal plane in the presence of a surface wave.
The structure of a surface wave resonator is an electroacoustic transducer T with interdigital combs surrounded on either side by Bragg mirrors M1 and M2. FIG. 3 illustrates the electrodes of a surface wave resonator seen from above.
At the resonance frequency, the condition of synchronism between the reflectors is satisfied making it possible to obtain a coherent addition of the different reflections which occur under the reflectors. A maximum of acoustic energy is then observed within the resonant cavity and, from an electrical point of view, a maximum of amplitude of the current admitted by the transducer is observed. The electrical conductance (real part of the admittance which, multiplied by the voltage, gives the current), a function of the frequency, therefore admixed, at the resonance frequency, a maximum as illustrated in FIG. 4.
When connected to an antenna, the resonators can be interrogated via electromagnetic waves, that is to say that it is possible to determine their resonance frequency. For that, an interrogation method is used that is close to that of RADAR as illustrated in FIG. 5.
An electromagnetic pulse of sufficient duration is transmitted at a frequency F0 and forces the resonator to oscillate at this frequency, and this is the so-called “transmission” phase. The closer the transmitted frequency is to the resonance frequency of the resonator (condition of synchronism in the Bragg mirrors), the more energy the resonator accumulates in the acoustic cavity. For the duration of the transmitted pulse, the resonator is charged, accumulating energy. Then, after a brief transient state, the resonator is discharged into the antenna which is connected to it, transmitting a decreasing exponential at its natural oscillation frequency Fr, that is to say at the resonance frequency. The received power of the decreasing exponential is then measured, and this is the so-called “reception” phase. The complete operation is repeated by varying the interrogation frequency F0 and the maximum power measured or estimated corresponds to the resonance frequency. This resonance frequency depends in particular on the temperature and on the strain to which the SAW device is subjected.
So as to be free of certain RF disturbances (distance between the sensor and the transmission antenna in particular) and of certain problems due to the aging of the sensor (drift of the frequencies over time for example), the latter is generally composed of a minimum of two resonators. That makes it possible to use the frequency difference between the two resonators to calculate the physical quantity measured, such as the temperature for example.
A certain number of works have already been carried out in the field of temperature measurement on moving objects.
For example, the patent U.S. Pat. No. 6,964,518 describes a device of glove finger type for measuring temperature inside a moving mechanical part. According to this patent, the temperature sensor contains an element sensitive to surface acoustic waves, commonly called SAW, exhibiting a transfer function dependent on the temperature. The proposed solution is of delay line type. One of the drawbacks with this type of solution is the maximum interrogation distance (defined as the distance between the antenna associated with the sensor and the antenna associated with the reader) which is less (in the context of compliance with the standards) than the distances accessible in the case of sensitive elements of resonator type. This last point in particular makes it difficult to interrogate several sensors with a single interrogation antenna.
The patent US2008259995 describes a temperature probe for domestic application which also incorporates a single sensitive element, but one that is of resonator type. The probe can be used to measure the internal temperature of food while being baked in an oven for example. In this case also, the position of the sensor in relation to its environment will be variable from one bake to another. Nevertheless, the use of a single resonator makes the measurement of the temperature sensitive to the frequency pulling effect due to the variation of the impedance of the antenna connected to the SAW sensor (for example linked to the relative movement of the antenna in a metal environment).
It should also be noted that the use of a single resonator does not make it possible to be free of the dependency of the temperature measurement on the drift of the local oscillator with which the reader is equipped.
For the same type of domestic application, the patent US20120143559 teaches a system which comprises a passive probe with a temperature sensor which comprises two resonators. This differential structure, subject to observing certain maximum deviations between the values of the elements of the equivalent circuits of BVD (Butterworth-Van Dyke equivalent model) type of each of the two resonators, theoretically makes it possible to have a temperature measurement independent of the position of the temperature probe in the oven. It has been found that if certain precautions are not taken in the design of the antenna connected to the sensor, an aberrant temperature measurement can nevertheless still occur.
It is recalled hereinbelow that the frequency response of a single-port resonator of SAW resonator type can be modelled using a Butterworth-Van Dyke (BVD) equivalent model as illustrated in FIG. 6 using motional elements Rm, Lm, Cm, and a static capacitor Co.
FIGS. 7a and 7b present the measurement-BVD model superposition for the real and imaginary parts of the impedance of an SAW sensitive element comprising two resonators meeting the conditions given in the patent application DE102009056060 A1.
The values of the parameters R, L, C, C0 of this differential sensor are as follows:                R1=36.75Ω, L1=181.84 μH, C1=0.74 fF        R2=37.75Ω, L2=197.45 μH, C2=0.68 fF        C0=5 pF        
In this patent application, it is taught that, to minimize the frequency pulling, it is best to have variations ΔR, ΔL and ΔC below threshold values.
Nevertheless, and generally, there is no single unique impedance matching condition between the antenna and the SAW sensor, but an infinity thereof. In most of the applications (industrial, domestic), the antennas (reader and sensor) are located in near field or else in environments where a coupling between the antennas exists. The impedance seen by the SAW sensor is therefore, in these conditions, a function of the impedance of the reader antenna, of the antenna which is directly connected to it and of the coupling between these two antennas.
FIG. 8 illustrates the equivalent circuit seen at the terminals of the SAW sensor connected to a sensor antenna coupled to a reader antenna, in the case of the sensor comprising two resonators.
Maximizing the transfer of energy to the SAW sensor (and therefore maximizing the interrogation distance) amounts to maximizing the power PSAW dissipated in the SAW sensor with PSAW corresponding to the received power/transmitted power ratio and defined as follows:
                                          P            SAW                    ⁡                      (                          ω              ,                                                Z                  T                                ⁡                                  (                  ω                  )                                                      )                          =                              1            2                    ⁢                                                                                  E                  T                                ⁡                                  (                  ω                  )                                                                                                  Z                    T                                    ⁡                                      (                    ω                    )                                                  +                                                      Z                    SAW                                    ⁡                                      (                    ω                    )                                                                                            ⁢                      Re            ⁡                          (                                                Z                  SAW                                ⁡                                  (                  ω                  )                                            )                                                          Equation        ⁢                                  ⁢                  (          1          )                    in which:                ET(ω) represents the electromotive force of the Thevenin equivalent generator which depends in particular on the impedance of the reader antenna and on the coupling between the two antennas;        ZT(ω) represents the impedance of the Thevenin equivalent generator which depends in particular on the impedance of the sensor antenna, of the reader antenna and of the coupling between the two antennas;        ZSAW(ω) is the impedance of the sensor;        ω=2πf is the pulsing with f for frequency.        
According to the equivalent circuit of FIG. 8, it is therefore the equivalent impedance seen by the SAW sensor which has to fulfil the impedance matching condition (maximization of transmitted power in ZSAW).
The Applicant has studied the trend of the power Psaw as a function of the frequency (x axis) and of the conjugate imaginary part of ZT (y axis) for a real part of ZT of 5Ω with the sensor with two resonators bearing out the criteria of the patent DE102009056060 A1 cited previously. The results are reported in FIG. 9.
Through this example, it can be seen that, in the case where the real part of ZT is low (5Ω), a good link budget is obtained overall. Indeed, in this case, the maximum value of PSAW is close to 0 dB (vertical scale in grey levels).
It is nevertheless observed in this case that, depending on the value of the imaginary part of ZT, it is possible to obtain: an acceptable measurement of both resonances (case where Im (ZT)*=25Ω for example).
On the other hand, for a value of Im (ZT)*=−68Ω, the differential measurement is no longer possible because the frequency response of the differential sensor is then reduced to a single peak and the result of its operation leads to an aberrant temperature. This is an extreme case of frequency pulling where the temperature measurement is impossible.
These two cases appear clearly in FIG. 10 which presents the curves in two dimensions associated with these two particular cases:                the curve (a) relates to the frequency response of the SAW differential sensor with Re(ZT), Im(ZT)˜(5, −25);        the curve (b) relates to the frequency response of the differential sensor with Re(ZT),Im(ZT)˜(5, 68).        
It is therefore essential not to have environment parameters resulting in aberrant measurements.
And in all these cases however, the metal environment in particular around the antenna associated with the sensor must be taken into account because it generates a dependency on the impedance of the Thevenin equivalent generator and therefore a risk of being within a zone where the temperature measurement is aberrant.
The variations of parameters such as the magnetic permeability, the electrical permittivity or the electrical conductivity which generate variations ZT have an impact on the value of the parameter PSAW.
It is therefore possible to reformulate the equation (1) as the equation (2) as follows:PSAW(ω,μ,ε,σ)=½[ET(ω,μ,ε,σ)/(ZT(ω,μ,ε,σ)+ZSAW(ω,μ,ε,σ))]2Re(ZSAW(ω,μ,ε,σ))]  (2)